Chapter 2.5, Problem 31E

(a)

To determine

To graph: A scatter plot of the data with $x$ as the number of years past 2000 and $y$ as the gross domestic product (GDP) in billions of dollars.

(b)

To determine

A quadratic equation that best fits the data

$\begin{array}{cccc}\text{Year}& \text{GDP}& \text{Year}& \text{GDP}\\ \text{2000}& \text{9143}& \text{2040}& \text{79,680}\\ \text{2005}& \text{12,145}& \text{2045}& \text{103,444}\\ \text{2010}& \text{16,174}& \text{2050}& \text{133,925}\\ \text{2015}& \text{21,270}& \text{2055}& \text{173,175}\\ \text{2020}& \text{27,683}& \text{2060}& \text{224,044}\\ \text{2025}& \text{35,919}& \text{2065}& \text{290,042}\\ \text{2030}& \text{46,765}& \text{2070}& \text{375,219}\\ \text{2035}& \text{61,100}& & \end{array}$

(c)

To determine

A cubic equation that best fits the data

$\begin{array}{cccc}\text{Year}& \text{GDP}& \text{Year}& \text{GDP}\\ \text{2000}& \text{9143}& \text{2040}& \text{79,680}\\ \text{2005}& \text{12,145}& \text{2045}& \text{103,444}\\ \text{2010}& \text{16,174}& \text{2050}& \text{133,925}\\ \text{2015}& \text{21,270}& \text{2055}& \text{173,175}\\ \text{2020}& \text{27,683}& \text{2060}& \text{224,044}\\ \text{2025}& \text{35,919}& \text{2065}& \text{290,042}\\ \text{2030}& \text{46,765}& \text{2070}& \text{375,219}\\ \text{2035}& \text{61,100}& & \end{array}$.

(d)

To determine

The better fitting model out of cubic and quadratic models for the data

$\begin{array}{cccc}\text{Year}& \text{GDP}& \text{Year}& \text{GDP}\\ \text{2000}& \text{9143}& \text{2040}& \text{79,680}\\ \text{2005}& \text{12,145}& \text{2045}& \text{103,444}\\ \text{2010}& \text{16,174}& \text{2050}& \text{133,925}\\ \text{2015}& \text{21,270}& \text{2055}& \text{173,175}\\ \text{2020}& \text{27,683}& \text{2060}& \text{224,044}\\ \text{2025}& \text{35,919}& \text{2065}& \text{290,042}\\ \text{2030}& \text{46,765}& \text{2070}& \text{375,219}\\ \text{2035}& \text{61,100}& & \end{array}$.